Apparatus and method for adaptive i/q imbalance compensation

ABSTRACT

An I/Q imbalance compensation block of a RF receiver for compensating an imbalance between an in-phase component and a quadrature component of an RF signal is disclosed. The compensation block includes a conjugation block; an adaptive finite impulse response (FIR) filter; and an adder. The filter use filter coefficients iteratively updated at least partly in response to a compensated digital signal. The filter can have a complex number for at least one, but not all of filter taps, and real numbers for other filter taps. The filter can be provided with adaptation step sizes different from filter tap to filter tap. The filter can also be provided with an adaptation step size(s) varying over time. The filter can also be provided with an adaptation step size(s) divided by the square norm of the compensated signal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to APPARATUS AND METHOD FOR ADAPTIVE I/QIMBALANCE COMPENSATION (Inventor: Raju Hormis; Atty. Docket No.ADINC.095A, filed on even date herewith), the disclosure of which isincorporated by reference in its entirety.

BACKGROUND

1. Field

Embodiments of the invention relate to electronic devices, and moreparticularly, in one or more embodiments, to radio frequency receivers.

2. Description of the Related Technology

Many electronic systems operate with radio-frequency (RF) signals. Suchelectronic systems can include an RF receiver that processes a wirelessor wired signal (for example, a radio frequency signal) received via awireless medium, such as air, or over a wire, such as a copper cable. AnRF receiver can include various components to amplify and/or filter anRF signal to recover original data carried by the RF signal.

Referring to FIG. 1, a conventional direct-conversion radio frequency(RF) receiver system will be described below. The illustrated system 100includes an antenna 101, an input stage structure 110, an input matchingnetwork 120, a low noise amplifier (LNA) 130, a first mixer 140 a, asecond mixer 140 b, a local oscillator 142, a phase shifter 144, a firstlow pass filter (LPF) 150 a, a second low pass filter 150 b, a firstanalog-to-digital converter (ADC) 160 a, a second analog-to-digitalconverter (ADC) 160 b, an adaptive I/Q compensation filter 170, an adder180, and a baseband module 190. The adaptive I/Q compensation filter 170and the adder 180 can be collectively referred to as an “I/Qcompensation module” or “I/Q compensation block” in the context of thisdocument. In an instance in which the receiver system is used forprocessing a wired signal, the antenna 101 can be omitted.

Since there are two mixers operating with 90° phase offset, the RFreceiver system 100 can be referred to as using “quadrature” reception.The PQ compensation module can be used with super-heterodyne receivers,or any other RF receiver that employs quadrature reception, even if thisquadrature operation occurs in only one stage of the RF receiver.

The antenna 101 is configured to receive an RF signal. The antenna 101can be any suitable antenna for wireless signal reception. The antenna101 provides the received wireless signal to the input stage structure110.

The input stage structure 110 serves to receive and process the RFsignal. The input stage structure 110 can include, for example, anantenna interface circuit to interface with the antenna 101, and afilter (for example, a band pass filter) to filter out signals outsideof a signal band of interest. The input stage structure 110 generates afirst processed signal, which is provided as an input to the inputmatching network 120.

The input matching network 120 serves to improve power transfer from theinput stage structure 110 to the low noise amplifier 130, and to reducesignal reflection from the low noise amplifier 130. Further, the inputmatching network 120 can serve to improve the noise performance of thelow noise amplifier 130. The input matching network 120 is configured tomatch the impedance of the low noise amplifier 130 with the impedance ofthe structure (for example, the input stage structure 110 and theantenna 101) on the opposite side of the input matching network 120 fromthe low noise amplifier 130. The input matching network 120 receives thefirst processed signal from the input stage structure 110, and generatesa second processed signal z(t), which is provided as an input to the lownoise amplifier 130.

The low noise amplifier 130 serves to amplify the second processedsignal z(t) from the input matching network 120 to generate an amplifiedsignal, and provides the amplified signal to the first and second mixers140 a, 140 b. The low noise amplifier 130 is configured to amplify arelatively weak signal with a gain such that the effect of noise onsubsequent stages of the receiver system 100 is reduced.

The first mixer 140 a serves to mix the amplified signal from the lownoise amplifier 130 and a first local frequency signal LOT from thephase shifter 144 to generate a first mixed signal. The first mixedsignal can include the fundamental frequencies of the current signal,the first local frequency signal, harmonics thereof, and intermodulationproducts. The second mixer 140 b serves to mix the amplified signal fromthe low noise amplifier 130 and a second local frequency signal LOQ fromthe phase shifter 144 to generate a second mixed signal. The secondmixed signal can include the fundamental frequencies of the currentsignal, the second local frequency signal, harmonics thereof, andintermodulation products.

In the illustrated example, the first local frequency signal LOI can beused to process in-phase (I) components of the received signal while thesecond local frequency signal LOQ can be used to process quadrature (Q)components of the received signal. Ideally, the first and second localfrequency signals LOI, LOQ should have a phase difference of 90 degreesfrom each other. The phase shifter 144 is configured to generate such aphase difference, using a local oscillation signal from the localoscillator 142. These components can also exist in other types of RFreceivers, such as super-heterodyne or low-IF receivers.

The first and second low pass filters 150 a, 150 b serve to filter thefirst and second mixed signals, respectively, and provide the filteredmixed signals to the first and second analog-to-digital converters 160a, 160 b, respectively. The first and second low pass filters 150 a, 150b are for anti-aliasing, and pass frequencies up to some cut-offfrequency. These filters block higher frequencies beyond this cut-offfrequency.

The first and second analog-to-digital converters 160 a, 160 b serve toconvert the filtered mixed signals from analog form into a digitalsignal x[n]. The first mixer 140 a, the first LPF 150 a, and the firstADC 160 a form an in-phase or I path. The second mixer 140 b, the secondLPF 150 b, and the second ADC 160 b form a quadrature-phase or Q path.The first and second analog-to-digital converters 160 a, 160 b canprovide the digital signal x[n] as an input to the adaptive filter 170and the adder 180. The output of the first ADC 160 a forms the realnumber portion of the digital signal x[n], and the output of the secondADC 160 b forms the imaginary number portion of the digital signal x[n].

The adaptive filter 170 is configured to generate a compensation signalto compensate for an imbalance between the I path and the Q path. Suchan imbalance can be referred to as “I/Q imbalance” or “I/Q mismatch” inthe context of this document, and will be described later in detail. Theadaptive filter 170 can use a feedback signal from the adder 180, andthe digital signal x[n] to generate the compensation signal that is tobe provided to the adder 180.

The adder 180 is configured to add the digital signal x[n] and thecompensation signal, and provides the compensated signal to the basebandmodule 190. The baseband module 190 receives the compensated signal fromthe adder 180, and performs digital signal processing on the signal. Thedigital signal processing can include, for example, demultiplexing anddecoding.

In an RF receiver such as a direct-conversion receiver, I/Q imbalanceoccurs, for example, when the transfer function of the I path of thereceiver is different from that of the Q path of the receiver, and/orwhen the phase relationship between the two paths is not quite 90degrees. Such imbalance occurs due to imperfections and variability ofthe analog components of an RF receiver, such as the filters, mixers,amplifiers, and ADCs. Sources of such imbalances include, but are notlimited to, gain and phase mismatch of the mixers, frequency responsesof low pass filters, gain and offset of ADCs, ADC-clock timing mismatch,and a non-linear I/Q imbalance. I/Q imbalance is typically unavoidableusing state-of-art analog circuit implementations.

I/Q imbalance can adversely affect the performance of an RF receiver.For example, I/Q imbalance can decrease the image rejection ratio (IRR)of an RF receiver down to, for example, 20-40 dB, resulting in crosstalkor interference between mirror frequencies. Thus, I/Q imbalance reducesthe signal-to-noise ratio of the receiver 100, and increase the numberof bit errors for a given data rate. Thus, I/Q imbalance needs to bereduced or cancelled.

I/Q imbalance can produce an undesired image signal, which falls withinthe band of interest. The term “image signal” refers to an undesiredsignal at frequencies occupied by the desired input signal. I/Qimbalance is a potential source of interference to proper reception. Theterm “image rejection ratio” is a measure of image strength relative todesired signal, and can refer to a ratio of (a) power of the desiredsignal to (b) power of the image signal. The image rejection ratio isusually expressed in decibels (dB). A desired IRR performance can be atleast 45 dB, for example, in cable-modem applications where the desiredbaseband signal occupies 50-70 MHz of bandwidth.

There have been various attempts to reduce or eliminate I/Q balance fromRF receivers. Among others, digital signal processing techniques havebeen used to reduce I/Q imbalance. Some of these techniques focus onfrequency-independent I/Q imbalance compensation in specificarchitectures and assume certain modulation schemes possibly combinedwith some known pilot or training data. Other techniques attempt tocompensate for frequency-dependant imbalances, assuming known pilot dataor using interference cancellation (IC) or blind signal separation (BSS)principles.

Among the techniques for frequency-dependent I/Q imbalance compensation,Anttila et al., “Circularity-Based I/Q Imbalance Compensation inWideband Direct-Conversion Receivers,” IEEE Transactions on VehicularTechnology, Vol. 57, No. 4, pp. 2099-2113 (July 2008), presents a blind(non-data-aided) circularity-based compensation of frequency-dependentI/Q imbalances in RF receivers.

Referring to FIG. 2A, an I/Q compensation module disclosed by Anttila etal. will be described below. The illustrated I/Q compensation module 200includes a first node 201, a second node 202, a complex conjugationblock 210, an adaptive filter 220, a delay element 225, a filteradaptation block 227, and an adder 230. A digital signal x[n] isprovided to the first node 201 from the I and Q paths of a receiver,such as the I and Q paths of FIG. 1. The digital signal x[n] is providedto the adder 230 and the conjugation block 210.

In the context of this document, “n” denotes a discrete-time index,where the time-interval between indices can be found from the samplingrate. In the context of this document, a discrete-time sequence ofsamples “x” is referred to as “x[n].” For simplicity of notation, “x[n]”can also be used to indicate the value of the sequence “x” at time-index“n.” Vectors in boldface, such as x_(n), will be used to refer to thevector at time-index “n.”

The conjugation block 210 is configured to change the polarity of theimaginary number part of the digital signal x[n], thereby generating acomplex conjugate signal x*[n] of the digital signal x[n]. For example,the digital signal x[n] can be a sequence of complex numbers. Forexample, let one sample in the sequence be expressed as a+jb, in which ais the real number part, jb is the imaginary number part, and jcorresponds to the square root of −1. The complex conjugate x*[n] hasthe same real part and has an imaginary part having the same magnitudeand the opposite sign. In the example above, the complex conjugate canbe expressed as a−jb.

The adaptive filter 220 can be a finite impulse response (FIR) filter,whose coefficients at time-index “n” can be expressed as the vectorw_(n). The FIR filter is a type of a discrete-time filter. The FIRfilter can generate an output digital sequence v[n] as expressed inEquation 1 below.

v[n]=w _(n)[0]x[n−N+1]+w _(n)[1]x[n−N]+ . . . +w _(n) [i]x[n−N+i]+ . . .+w _(n) [N−1]x[n]  Equation 1

In Equation 1, variable x[n] is the input signal, and variable v[n] isthe output signal. Weights w_(n)[i], (i=0, 1, 2, . . . , N−1) are filtercoefficients at time “n,” also known as tap weights. N is the filterorder or length, and an (N+1)th order filter has N terms, each of whichcan be referred to as a tap. For example, weight w_(n)[0] can bereferred to as a first tap at time “n,” which can correspond to a tapthat is not delayed. Weight w_(n)[1] can be referred to as a second tap.w_(n)[N−1] can be referred to as an N-th tap.

The adaptation filter 220 receives a feedback signal λ y_(n) y[n] fromthe adder 230 via the delay element 225 and the filter adaptation block227. In the illustrated example, an output signal y[n] from the adder230 is delayed by the delay element 225. The amount of a delay providedby the delay element 225 can be at least one sample. The delayed outputsignal is provided to the filter adaptation block 227, which generatesthe feedback signal λ y_(n) y[n]. The feedback signal λ y_(n) y[n] isused by the adaptive filter 220 to generate a compensation signal to beadded to the input signal x[n] at the adder 230 to cancel or reduce I/Qimbalance.

The adaptive filter 220 is configured to perform a complex-convolutionoperation (*) on the conjugate signal x*[n] with the adaptive filtersignal w_(n) to generate a compensation signal expressed as x*[n]*w_(n).The convolution operation can be computed as the sum of the product ofthe two sequences after one is reversed and shifted on the time axis.The adaptive filter w_(n) can be iteratively updated as in Equation 2below.

w _(n+1) =w _(n) −λy _(n) y[n]  Equation 2

In Equation 2, y[n] is the compensated signal value at time “n.” Thisvalue can be expressed as y[n]=x[n]+v[n]=w_(n) ^(T)x_(n), wherein w_(n)Δ [w_(n)[0], w_(n)[1], w_(n)[2], . . . , w_(n)[N−1]]^(T) denotes thevector of coefficients (alternatively “filter coefficients”) of thecompensator at time index n, and the vector x_(n) Δ[x[n−N+1], x[n−N], .. . , x[n]]^(T). λ denotes the adaptation step size or adaptation rate,and y_(n) Δ [y[n], y[n−1], . . . , y[n−N+1]]^(T).

The adder 230 adds the compensation signal to the digital signal x[n],and provides the compensated signal y[n] to the baseband module 190(FIG. 1) of the receiver. The compensated signal sequence y[n] isprovided as a feedback signal to the adaptive filter 220 through thedelay element 225 and the filter adaptation block 227.

The technique described in the above example is blind to the receivedbaseband signal, which is useful since a training signal need not beapplied at the receiver input. The technique is adaptive in that itaccounts for time-varying mismatches. The technique is alsofrequency-selective, and thus can be suitable for correction of widebandchannels.

Equation 2, above, indicates that the technique determining filtercoefficients w_(n) blindly (i.e., without knowledge of the basebandsignal) and adaptively by employing the signal “properness” property,that is, determining if y[n] is a proper signal sequence, whichindicates that y[n] and y*[n] are uncorrelated. In the technique ofAnttila et al., λ is a fixed training coefficient selected by the user.After convergence, the signal y[n] should exhibit the conditionexpressed in Equation 3 below, in which E denotes expected valueoperator (or expectation operator) that provides the long-run average.

E[y[n−i],y[n]]=0,where i=0,1, . . . N−1.  Equation 3

SUMMARY

In one embodiment, an apparatus includes a finite impulse response (FIR)filter configured to filter a version of a digital signal to generate acompensation signal, wherein the FIR filter has X real number filtercoefficients and Y imaginary number coefficients, wherein Y is less thanX, wherein the digital signal comprises a digital representation of ademodulated in-phase and quadrature phase component of a radio frequency(RF) signal. The apparatus also includes an adder configured to sumanother version of the digital signal and a version of the compensationsignal to generate a balanced digital signal that has an improved imagerejection ratio versus the digital signal. One of the versions of thedigital signal or the version of the compensation signal is a complexconjugate of the digital signal or a complex conjugate of thecompensation signal, respectively, and the others are not the complexconjugates, wherein the FIR filter and the adder comprise electronichardware.

In another embodiment, a method of improving an image rejection ratio ofa digital signal having demodulated in-phase and quadrature-phasecomponents of a radio frequency signal is provided. The method includesfiltering a version of the digital signal with a finite impulse response(FIR) filter to generate a compensation signal, wherein the FIR filterhas X real number filter coefficients and Y imaginary numbercoefficients, wherein Y is less than X, wherein filtering is implementedby hardware or by instructions implemented by a processor. The methodalso includes generating a complex conjugate of the digital signal orthe compensation signal; and summing another version of the digitalsignal and a version of the compensation signal to generate a balanceddigital signal that has an improved image rejection ratio versus thedigital signal, wherein one of the versions of the digital signal andthe version of the compensation signal corresponds to a complexconjugate of the digital signal or the compensation signal,respectively, and the others are not the complex conjugates.

In yet another embodiment, an apparatus includes an (N+1)-th orderfinite impulse response (FIR) filter configured to filter a version of adigital signal to generate a compensation signal, wherein the FIR filterhas N taps, N real number filter coefficients, and N−1 or fewerimaginary number coefficients, wherein the digital signal comprises adigital representation of a demodulated in-phase and quadrature phasecomponent of a radio frequency (RF) signal. The apparatus also includesmeans for generating a complex conjugate of the digital signal or thecompensation signal; and means for summing another version of thedigital signal and a version of the compensation signal to generate abalanced digital signal that has an improved image rejection ratioversus the digital signal. One of the versions of the digital signal andthe version of the compensation signal corresponds to a complexconjugate of the digital signal or the compensation signal,respectively, and the others are not the complex conjugates.

In yet another embodiment, an apparatus includes a finite impulseresponse (FIR) filter configured to filter a version of a digital signalto generate a compensation signal, wherein the FIR filter has X realnumber filter coefficients and X imaginary number coefficients, whereinat least one, but not all, of the imaginary number coefficients is 0,wherein the digital signal comprises a digital representation of ademodulated in-phase and quadrature phase component of a radio frequency(RF) signal. The apparatus also includes an adder configured to sumanother version of the digital signal and a version of the compensationsignal to generate a balanced digital signal that has an improved imagerejection ratio versus the digital signal. One of the versions of thedigital signal or the version of the compensation signal is a complexconjugate of the digital signal or a complex conjugate of thecompensation signal, respectively, and the others are not the complexconjugates, wherein the FIR filter and the adder comprise electronichardware.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic block diagram illustrating a conventional radiofrequency (RF) receiver.

FIG. 2A is a schematic block diagram illustrating a conventional I/Qimbalance compensation module.

FIG. 2B is a graph of impulse responses of I/Q imbalance obtained fromthe adaptive filter of FIG. 2A.

FIG. 3 is a schematic block diagram illustrating an I/Q imbalancecompensation module according to one embodiment.

FIG. 4A is a schematic block diagram illustrating an I/Q imbalancecompensation module according to another embodiment.

FIG. 4B is a flowchart illustrating a method of generating variableadaptation step sizes according to one embodiment.

FIG. 5 is a schematic block diagram illustrating an I/Q imbalancecompensation module according to yet another embodiment.

FIG. 6 is a graph showing image rejection ratio performance of an RFreceiver without I/Q imbalance compensation.

FIG. 7 is a graph showing image rejection ratio performances of aconventional I/Q imbalance compensation module and an I/Q imbalancecompensation module according to one embodiment.

FIG. 8 is a schematic block diagram illustrating an I/Q imbalancecompensation module according to another embodiment.

FIG. 9 is a schematic block diagram illustrating an I/Q imbalancecompensation module according to yet another embodiment.

FIG. 10 is a schematic block diagram illustrating an I/Q imbalancecompensation module according to yet another embodiment.

DETAILED DESCRIPTION OF EMBODIMENTS

The following detailed description of certain embodiments presentsvarious descriptions of specific embodiments of the invention. However,the invention can be embodied in a multitude of different ways asdefined and covered by the claims. In this description, reference ismade to the drawings where like reference numerals indicate identical orfunctionally similar elements.

Improved Adaptive Filter by Model Reduction Technique

In connection with the above-described technique of Anttila et al., theinstantaneous product y[n] y[n] is an estimate of correlation strength,and thus an estimate of strength of image y*[n] present in y[n]. Thetechnique iteratively adapts the coefficient w_(n) to drive the imagesignal to 0. Since these iterations cannot take place instantaneously,there is an adaptation period that is called “convergence time.”

Anttila, et al., obtained about 40-55 dB of imbalance rejection on a 10MHz receiver. However, Applicant recognized that, for wideband receivers(for example, on RF receivers with 50-100 MHz of bandwidth) with severeI/Q imbalance, the technique is not only slow to converge, but also doesnot exhibit a minimum desired image rejection ratio (for example, atleast about 45 dB) even after convergence. Further, the Anttila'stechnique is computationally expensive.

In one embodiment, the compensation filter is modeled as closely aspossible to the impulse response of the I/Q imbalance. Although theimbalance typically cannot be known or assumed before experiencing theactual imbalance in the receiver, Applicant recognized that there arecertain general patterns. When the analog low-pass filters have all poledesigns (for example, Butterworth filters or Chebyshev filters), theimaginary part of the I/Q imbalance is typically negligibly small inrelation to the real parts of the response. Typically, the onlyexception is at the first tap (n=0), in which the imaginary part of theresponse is relatively significant.

An example of such a pattern is shown in FIG. 2B, which illustratesexamples of filter coefficients. In FIG. 2B, at a first tap (n=0), thecomplex number is about −0.053-j0.044, that is, the real part of thecomplex number is about −0.053, and the imaginary part of the complexnumber is −0.044. At n=1, the complex number is about −0.042+j0. At n=2,the complex number is about −0.009+j0. At n=3, the complex number isabout 0.01+j0. At n=4, the complex number is about 0.007+j0. At n=5, thecomplex number is about −0.003+j0. At n=6, the complex number is about−0.005+j0. At n=7, the complex number is about −0.001+j0. At n=8, thecomplex number is about 0.003+j0. At n=9, the complex number is about0.001+j0. At n=10, the complex number is about −0.001+j0. The complexnumber converges to 0+j0 roughly at n=16. A skilled artisan willappreciate that actual values of taps can vary widely from chip to chipwhile having the above-described general pattern.

In recognition of the above pattern, in one embodiment, a finite impulseresponse adaptive filter in which only the first tap of the filter is acomplex number, and the other taps of the filter are purely real numbersis disclosed. In general, an N^(th) order filter according to oneembodiment of the invention has N+1 taps and N+1 real numbercoefficients, and fewer than N+1 imaginary number coefficients.Alternatively, a FIR filter having more real number coefficients thanimaginary number coefficients is used. For example, only the first tapand a few immediately next taps of the filter are complex numbers, andthe other taps of the filter are purely real numbers. Advantageously,these configurations speed up convergence in addition to reducing thecomplexity of the filter. In the context of this document, theseconfigurations can be referred to as “model reduction techniques.”

Referring to FIG. 3, an I/Q imbalance compensation module according toone embodiment will be described below. The illustrated I/Q imbalancecompensation module 300 includes a first node 301, a second node 302, acomplex conjugation block 310, an adaptive filter 320, a delay element325, a filter adaptation block 327, and an adder 330. In one embodiment,each of the conjugation block 310, the adaptive filter 320, the delayelement 325, the filter adaptation block 327, and the adder 330 can beimplemented in firmware or hardware. The conjugation block 310, theadaptive filter 320, and the adder 330 can operate real time. The delayelement 325 and the filter adaptation block 327 can operate real time.However, the filter adaptation block 327 can have some latency, i.e., itmay take a few sampling clock intervals to compute the first outputsample. However, every sample it outputs after the first sample can beat a sample clock interval.

A complex digital signal x[n] is provided to the first node 301 from theI and Q paths of a receiver, such as the I and Q paths of FIG. 1. Thedigital signal x[n] is provided to the adder 330 and the conjugationblock 310. Other details of the first node 301, the second node 302, theconjugation block 310, the delay element 325, the filter adaptationblock 327, and the adder 330 can be as described above in connectionwith the first node 201, the second, node 202, the conjugation block210, the delay element 225, the filter adaptation block 227, and theadder 230, respectively, of FIG. 2A. In an alternative embodiment, theorder of operation for the complex conjugation block 310 and theadaptive filter 320 are interchanged, as will be described in connectionwith FIG. 8.

In the illustrated embodiment, the adaptive filter 320 can be a finiteimpulse response (FIR) filter that serves to perform a convolutionoperation (*) on the conjugate signal x*[n] with the filter coefficientsw_(n) to generate a compensation signal expressed in x*[n]*w_(n). Whilethe above Equation 1 applies to the adaptive filter 320 of FIG. 3, theadaptive signal w_(n) can be iteratively updated for each tap, as inEquation 4 below.

w _(n+1) [i]=w _(n) [i]−λy[n]y[n−i] for i=0,1,2, . . . ,N−1  Equation 4

In Equation 4, i is the tap number of the finite impulse responseadaptive filter 320. Equation 4 indicates that the filter coefficient ofa tap is updated by subtracting a feedback value λ y[n] y[n−i] from thefilter coefficient of the tap at an immediately previous sampling time.The feedback value is generated from the output signal y[n] through thedelay element 325 and the filter adaptation block 327. λ is a fixedtraining coefficient selected, through trial and error, by the user. Thevalue of λ can vary widely, depending on the RF front-ends havingdifferent noise and/or I/Q imbalance.

Equation 2 can be expressed for each tap, as in Equations 4-1 to 4-Nbelow. The filter coefficient is applied to the conjugate value of theinput signal x[n] by a convolution operation to generate a value to beadded to the input signal x[n] to reduce or remove values contributingto I/Q imbalance.

$\begin{matrix}{\mspace{79mu} {{{Tap}\mspace{14mu} 0\text{:}\mspace{14mu} {w_{n + 1}\lbrack 0\rbrack}} = {{w_{n}\lbrack 0\rbrack} - {\lambda \; {y\lbrack n\rbrack}{y\lbrack {n - 0} \rbrack}}}}} & {{Equation}\mspace{14mu} 4\text{-}1} \\{\mspace{79mu} {{{Tap}\mspace{14mu} 1\text{:}\mspace{14mu} {w_{n + 1}\lbrack 1\rbrack}} = {{w_{n}\lbrack 1\rbrack} - {\lambda \; {y\lbrack n\rbrack}{y\lbrack {n - 1} \rbrack}}}}} & {{Equation}\mspace{14mu} 4\text{-}2} \\{\mspace{79mu} {{{{Tap}\mspace{14mu} 2\text{:}\mspace{14mu} {w_{n + 1}\lbrack 2\rbrack}} = {{w_{n}\lbrack 2\rbrack} - {\lambda \; {y\lbrack n\rbrack}{y\lbrack {n - 2} \rbrack}}}} {\vdots \mspace{230mu} \vdots} {\vdots \mspace{230mu} \vdots}}} & {{Equation}\mspace{14mu} 4\text{-}3} \\{{{{Tap}\mspace{14mu} N} - {1\text{:}\mspace{14mu} {w_{n + 1}\lbrack {N - 1} \rbrack}}} = {{w_{n}\lbrack {N - 1} \rbrack} - {\lambda \; {y\lbrack n\rbrack}{y\lbrack {n - N + 1} \rbrack}}}} & {{Equation}\mspace{14mu} 4\text{-}N}\end{matrix}$

In iteratively calculating Equation 4, only coefficient w_(n)[0] is acomplex number, and coefficients for the other taps, such ascoefficients w_(n)[1], w_(n)[2], w_(n)[3], w_(n)[N−1] are assumed to bepurely real numbers, ignoring their imaginary parts. Thus, in theEquations 4-1 to 4-N above, coefficient w_(n)[0] for the Tap 0 is acomplex number having both the real and imaginary parts. However,coefficients w_(n)[1], w_(n)[2], . . . , w_(n)[N−1] for the Taps 1 to(N−1) are real numbers having no imaginary part. Thus, w_(n), which isused in the convolution operation of x*[n]*w_(n), can be expressed as inEquation 5-1 below.

$\begin{matrix}{w_{n} = {\begin{pmatrix}{w_{n}\lbrack 0\rbrack} \\{w_{n}\lbrack 1\rbrack} \\\vdots \\{w_{n}\lbrack {N - 1} \rbrack}\end{pmatrix} = {\begin{pmatrix}{c_{0} + {jd}_{0}} \\c_{1} \\\vdots \\c_{N - 1}\end{pmatrix} = {\begin{pmatrix}c_{0} \\c_{1} \\\vdots \\c_{N - 1}\end{pmatrix} + {j\begin{pmatrix}d_{0} \\0 \\\vdots \\0\end{pmatrix}}}}}} & {{Equation}\mspace{14mu} 5\text{-}1}\end{matrix}$

When the coefficients w_(n)[0], w_(n)[1], w_(n)[2], w_(n)[3], . . . ,w_(n)[N−1] are used by the adaptive filter 320, an output from theadaptive filter 320 can be expressed as in Equation 5-2 below.

$\begin{matrix}\begin{matrix}{{v\lbrack n\rbrack} = {{{w_{n}\lbrack 0\rbrack}{x\lbrack {n - N + 1} \rbrack}} + {{w_{n}\lbrack 1\rbrack}{x\lbrack {n - N} \rbrack}} + \ldots +}} \\{{{{w_{n}\lbrack i\rbrack}{x\lbrack {n - N + i} \rbrack}} + \ldots + {{w_{n}\lbrack {N - 1} \rbrack}{x\lbrack n\rbrack}}}} \\{= {{( {c_{0} + {jd}_{0}} ){x\lbrack {n - N + 1} \rbrack}} + {c_{1}{x\lbrack {n - N} \rbrack}} + \ldots +}} \\{{{c_{i}{x\lbrack {n - N + i} \rbrack}} + \ldots + {{c_{N - 1}\lbrack {N - 1} \rbrack}{x\lbrack n\rbrack}}}}\end{matrix} & {{Equation}\mspace{14mu} 5\text{-}2}\end{matrix}$

As coefficient w_(n) has only a complex number for the first tap, thecomputational complexity of adaptation can be significantly reduced,compared to the technique of Anttila et al., thereby reducing theconvergence time. In other embodiments, the reduction in complexity ofcomputation of the adaptive coefficient determination can also be usedin an FIR filter having, for example, an equal number of real numbercoefficients and imaginary number coefficients by setting some of theimaginary number coefficients to zero.

In the illustrated embodiment, the adaptive filter 320 can includestorage 322 having multiple cells 324 for a plurality of real parts forthe tap coefficients, but only a single cell 326 for an imaginary partof the first tap (w_(n)[0]). In one embodiment, the storage 322 caninclude one or more registers. In another embodiment, the storage 322can be any suitable type of volatile or non-volatile memory devices.

Variable Adaptation Step Size for Adaptive Filter

In another embodiment, the adaptive filter of FIG. 2A can be providedwith different adaptation step sizes for different taps. In yet anotherembodiment, the adaptive filter of FIG. 2A can be provided with a singlevariable adaptation step size that can vary over time. In yet anotherembodiment, the adaptive filter of FIG. 2A can be provided withdifferent adaptation step sizes for different taps that vary over time.Each of these embodiments can be combined with the embodiment of FIG. 3with model reduction technique.

Referring to FIG. 4, an I/Q imbalance compensation module with anadaptive filter having variable adaptation step sizes according toanother embodiment will be described below. The illustrated I/Qimbalance compensation module 400 includes a first node 401, a secondnode 402, a complex conjugation block 410, an adaptive filter 420, adelay element 425, a filter adaptation block 427, an adder 430, anadaptation step size adaptor 440, and a controller 450. A digital signalx[n] is provided to the first node 401 from the I and Q paths of areceiver, such as the I and Q paths of FIG. 1. The digital signal x[n]is provided to the adder 430 and the conjugation block 410. Otherdetails of the first node 401, the second node 402, the conjugationblock 410, the delay element 425, the filter adaptation block 427, andthe adder 430 can be as described above in connection with the firstnode 201, the second node 202, the conjugation block 210, the delayelement 225, the filter adaptation block 227, and the adder 230,respectively, of FIG. 2A.

The adaptive filter 420 can be a finite impulse response (FIR) filterthat serves to perform a convolution operation (*) on the conjugatesignal x[n] with FIR coefficients w_(n) to generate a compensationsignal expressed in x*[n]*w_(n). In one embodiment, the configuration ofthe adaptive filter 420 can be the same as that of the adaptive filter220 of FIG. 2A except that the adaptation step size λ is replaced withvariable step size μ, which will be described below. In anotherembodiment, the configuration of the adaptive filter 420 can be the sameas that of the adaptive filter 320 of FIG. 3 except that the adaptationstep size λ is replaced with the variable step size μ.

Applicant recognized that the impulse response of the I/Q imbalance ofthe receiver exhibits an overall exponential decay. In one embodiment,the adaptive filter can be designed with dedicated adaptation step sizeμ for each tap. For example, μ (i) can be designated as μ for an i-thtap. The adaptive filter w_(n) can be iteratively updated as expressedin Equation 6 below.

w _(n+1)(i)=w _(n)(i)−μ(i)y[n]y[n−i]  Equation 6

When “i” refers to a tap that is purely real (i.e., not a complexnumber), although y[n] y[n−i] represents a multiplication of 2 complexnumbers, only the real part of the product y[n] y[n−i] is used inupdating the filter coefficient. The imaginary part of y[n] y[n−i] neednot be computed. This also reduces the computational complexity of thesystem.

In one embodiment, the adaptive filter 420 can have different μ per tapas in Equation 7 below.

μ(i)=μ(0)/2^(i)  Equation 7

In Equation 7, μ (i) is the adaptation step size of the i-th filtercoefficient, and μ (0) is the first filter coefficient. The adaptationstep sizes can be expressed in Equations 7-1 to 7-N below.

$\begin{matrix}{{\mu (1)} = {{\mu (0)}/2}} & {{Equation}\mspace{14mu} 7\text{-}1} \\{{\mu (2)} = {{{\mu (1)}/2} = {{\mu (0)}/4}}} & {{Equation}\mspace{14mu} 7\text{-}2} \\{{{\mu (3)} = {{{\mu (2)}/2} = {{\mu (0)}/8}}}\mspace{25mu} {\vdots \mspace{155mu} \vdots}} & {{Equation}\mspace{14mu} 7\text{-}3} \\{{\mu ( {N - 1} )} = {{{\mu ( {N - 2} )}/2} = {{\mu (0)}/2^{N - 1}}}} & {{Equation}\mspace{14mu} 7\text{-}N}\end{matrix}$

Thus, the adaptive filter 420 can be updated in accordance withEquations 8-1 to 8-N as applicable.

$\begin{matrix}{\mspace{79mu} {{{Tap}\mspace{14mu} 0\text{:}\mspace{14mu} {w_{n + 1}\lbrack 0\rbrack}} = {{w_{n}\lbrack 0\rbrack} - {{\mu (0)}{y\lbrack n\rbrack}{y\lbrack {n - 0} \rbrack}}}}} & {{Equation}\mspace{14mu} 8\text{-}1} \\{\mspace{79mu} {{{Tap}\mspace{14mu} 1\text{:}\mspace{14mu} {w_{n + 1}\lbrack 1\rbrack}} = {{w_{n}\lbrack 1\rbrack} - {{\mu (1)}{y\lbrack n\rbrack}{y\lbrack {n - 1} \rbrack}}}}} & {{Equation}\mspace{14mu} 8\text{-}2} \\{\mspace{79mu} {{{{Tap}\mspace{14mu} 2\text{:}\mspace{14mu} {w_{n + 1}\lbrack 2\rbrack}} = {{w_{n}\lbrack 2\rbrack} - {{\mu (2)}{y\lbrack n\rbrack}{y\lbrack {n - 2} \rbrack}}}}\mspace{104mu} {\vdots \mspace{225mu} \vdots}}} & {{Equation}\mspace{14mu} 8\text{-}3} \\{{{Tap}\mspace{14mu} n\text{:}\mspace{14mu} {w_{n + 1}\lbrack {N - 1} \rbrack}} = {{w_{n}\lbrack {N - 1} \rbrack} - {{\mu ( {N - 1} )}{y\lbrack n\rbrack}{y\lbrack {n - N + 1} \rbrack}}}} & {{Equation}\mspace{14mu} 8\text{-}N}\end{matrix}$

In another embodiment, μ's for the taps can be different from oneanother, while being different from those in Equations 7-1 to 7-N. Askilled artisan will appreciate that step sizes μ for taps can beadapted for a particular receiver.

The adaptation step size adaptor 440 serves to provide differentadaptation step sizes μ for the different taps of the adaptive filter430. In one embodiment, the adaptation step size adaptor 440 can includea look-up table 442 to store different values of the step size μ foreach tap, and can provide the values for components of the feedbacksignal y[n−N+i], i=0, 1 . . . , N−1 in Equations 8-1 to 8-N above. Inthe illustrated embodiment, the adaptation step size adaptor 440 isdepicted as being separate from the adaptive filter 420. In analternative embodiment, the adaptation step size adaptor 440 isintegrated with the adaptive filter 420.

The controller 450 serves to control the adaptive filter 420 and theadaptation step size adaptor 440 to perform the operations describedabove. In one embodiment, the adaptive filter 420 and the adaptationstep size adaptor 440 can be implemented by a digital circuit. Inanother embodiment, each of the conjugation block 410, the adaptivefilter 420, the delay element 425, the filter adaptation block 427, theadaptation step size adaptor 440, and the adder 430 can be implementedin firmware or hardware. The conjugation block 410, the adaptive filter420, and the adder 430 can operate real time. The delay element 425, thefilter adaptation block 427, and the adaptation step size adaptor 440can operate non-real time.

In the illustrated embodiment, the controller 450 is depicted as beingseparate from the adaptive filter 420 or the adaptation step sizeadaptor 440. In an alternative embodiment, the controller 450 can beintegrated with the adaptive filter 420 and/or the adaptation step sizeadaptor 440. In other embodiments, two or more of the delay element 425,the filter adaptation block 427, and the adaptation step size block 440can be integrated with one another.

In yet another embodiment, the adaptation step sizes of the adaptivefilter 420 can be varied over time. For example, the adaptation stepsize can have an initial value μ₀ at time t₀. At fixed time intervals,the adaptation step size can be decreased exponentially. For example,adaptation step size μ can be decreased from 10⁻³ to 10⁻¹⁰ at fixed timeintervals, such that μ₀=10⁻³ for time-index n=n₀ to n₁, μ₂=10⁻⁴ fromtime-index n₁ to n₂, and so on. The values of adaptation step sizesvarying over time: n, and the time-index boundaries n₀, n₁, . . . ,n_(n) can be stored in the look-up table 442.

In some embodiments, the adaptation step sizes vary over time, whilehaving different values for different taps as described above inconnection with Equations 7-1 to 7-N. In one embodiment, only μ (0) isvaried over time and other adaptation steps sizes, μ (1), μ (2), μ (3),. . . are advantageously computed based on μ (0) as shown in Equations7-1 to 7-N above. In an alternative embodiment, one or more ofcoefficients are independently computed.

Thus, values for coefficients for the taps can be efficiently computedto compensate for drift over time. For example, after a time intervalfrom n₀, the Equations 8-1 to 8-N can be changed as in Equations 9-1 to9-N. This configuration speeds up the convergence by orders ofmagnitude.

$\begin{matrix}{\mspace{79mu} {{{{Tap}\mspace{14mu} 0\text{:}\mspace{14mu} {w_{n + 1}\lbrack 0\rbrack}} = {{w_{n}\lbrack 0\rbrack} - {{\mu_{1}(0)}{y\lbrack n\rbrack}{y\lbrack {n - 0} \rbrack}}}},\mspace{79mu} {{{in}\mspace{14mu} {which}\mspace{14mu} {\mu_{1}(0)}} = {{\mu_{0}(0)} \times 10^{- 1}}}}} & {{Equation}\mspace{14mu} 9\text{-}1} \\\begin{matrix}{\mspace{79mu} {{{Tap}\mspace{14mu} 1\text{:}\mspace{14mu} {w_{n + 1}\lbrack 1\rbrack}} = {{w_{n}(1)} - {{\mu_{1}(1)}{y\lbrack n\rbrack}{y\lbrack {n - 1} \rbrack}}}}} \\{= {{w_{n}(1)} - {2^{- 1}{\mu_{I}(0)}{y\lbrack n\rbrack}{y\lbrack {n - 1} \rbrack}}}}\end{matrix} & {{Equation}\mspace{14mu} 9\text{-}2} \\{\begin{matrix}{\mspace{79mu} {{{Tap}\mspace{14mu} 2\text{:}\mspace{14mu} {w_{n + 1}\lbrack 2\rbrack}} = {{w_{n}\lbrack 2\rbrack} - {{\mu_{I}(2)}{y\lbrack n\rbrack}{y\lbrack {n - 2} \rbrack}}}}} \\{= {{w_{n}\lbrack 2\rbrack} - {2^{- 2}{\mu_{1}(0)}{y\lbrack n\rbrack}{y\lbrack {n - 1} \rbrack}}}}\end{matrix}\mspace{191mu} {\vdots \mspace{245mu} \vdots}} & {{Equation}\mspace{14mu} 9\text{-}3} \\\begin{matrix}{{{Tap}\mspace{14mu} n\text{:}\mspace{14mu} {w_{n + 1}\lbrack 3\rbrack}} = {{w_{n}\lbrack {N - 1} \rbrack} - {{\mu_{l}( {N - 1} )}{y\lbrack n\rbrack}{y\lbrack {n - N + 1} \rbrack}}}} \\{= {{w_{n}\lbrack {N - 1} \rbrack} - {2^{- {({N - 2})}}{\mu_{l}(0)}{y\lbrack n\rbrack}{y\lbrack {n - N + l} \rbrack}}}}\end{matrix} & {{Equation}\mspace{14mu} 9\text{-}N}\end{matrix}$

Referring to FIG. 4B, a method of varying adaptation step sizes for anadaptive filter according to one embodiment will be described below. Inthe illustrated embodiment, only μ (0) is varied over time and otheradaptation steps sizes, μ (1), μ (2), μ (3), . . . are advantageouslycomputed based on μ (0) as shown in Equations 7-1 to 7-N above. Themethod can be performed by, for example, the adaptation step sizeadaptor 440 of FIG. 4A.

In the illustrated embodiment, at step 481, an initial adaptation stepsize μ (0) is provided for the first tap. At step 482, adaptation stepsizes μ (1), μ (2), μ (3), . . . for other taps are generated based on μ(0). All the adaptation step sizes μ (0), μ (1), μ (2), μ (3), . . . areprovided to the adaptive filter for filtering at step 483. At step 484,a clock is checked to determine whether a preselected time interval haspassed. If so, the adaptation step size μ (0) for the first tap isupdated at step 485. In the illustrated embodiment, the value of μ (0)is reduced, and the reduced value is provided for computing the otheradaptation step sizes μ (1), μ (2), μ (3), at step 482. This process isrepeated until the filter is adapted for I/Q imbalance compensation.

Normalized Adaptation Step Size for Adaptive Filter

Referring to FIG. 5, an I/Q imbalance compensation module with anadaptive filter having a normalized variable adaptation step sizeaccording to yet another embodiment will be described below. Theillustrated I/Q imbalance compensation module 500 includes a first node501, a second node 502, a complex conjugation block 510, an adaptivefilter 520, a delay element 525, a filter adaptation block 527, an adder530, an adaptation step size adaptor 540, and an optional controller(not shown). In one embodiment, each of the conjugation block 510, theadaptive filter 520, the delay element 525, the filter adaptation block527, the adder 530, and the adaptation step size adaptor 540 can beimplemented in firmware or hardware. The conjugation block 510, theadaptive filter 520, and the adder 530 can operate real time. The delayelement 525, the filter adaptation block 527, and the adaptation stepsize adaptor 540 can operate non-real time.

A complex digital signal x[n] is provided to the first node 501 from theI and Q paths of a receiver, such as the I and Q paths of FIG. 1. Thedigital signal x[n] is provided to the adder 530 and the conjugationblock 510. Other details of the first node 501, the second node 502, theconjugation block 510, the delay element 525, the filter adaptationblock 527, and the adder 530 can be as described above in connectionwith the first node 201, the second node 202, the conjugation block 210,the delay element 225, the filter adaptation block 227, and the adder230, respectively, of FIG. 2A.

The adaptive filter 520 can be a finite impulse response (FIR) filterwith coefficients w_(n) that serves to perform a convolution operation(*) on the conjugate signal x*[n] to generate a compensation signalexpressed as x*[n]*w_(n). In one embodiment, the configuration of theadaptive filter 520 can be the same as that of the adaptive filter 220of FIG. 2A except that the adaptation step size is replaced with anadaptation step size normalized by received signal strength. Such anormalized adaptation step size can be denoted as λ/∥y_(n)∥². In anotherembodiment, the configuration of the adaptive filter 520 can be the sameas that of the adaptive filter 320 of FIG. 3 except that the adaptationstep size is replaced with the normalized step size λ/∥y_(n)∥². Thus,the adaptive signal w_(n) can be iteratively updated as expressed inEquations 10-a or 10-b below.

w _(n+1) =w _(n) −λy _(n) y[n]/∥y _(n)∥²  Equation 10-a

w _(n+1)(i)=w _(n)(i)−λy[n]y[n−i]/∥y _(n)∥², where i=0, 1, . . .N−1.  Equation 10-b

In the Equations 10-a and 10-b, ∥y_(n)∥² represents the squared-norm ofthe data vector y_(n), and can be expressed in Equation 11 below.

∥y _(n)∥²=(y[n]·y*[n]+y[n−1]·y*[n−1]+ . . .+y[n−N+1]·y*[n−N+1])/N  Equation 11

In Equation 11, N is the length of the filter, i.e., the number of taps.The adaptation step size is scaled by the norm or magnitude of the datavectory(n).

The adaptation step size adaptor 540 serves to provide the norm of theoutput data y(n) for the adaptive filter 530. The adaptation step sizeadaptor 540 can include a normalizer 550 to compute the norm. In theillustrated embodiment, the adaptor 540 is depicted as being separatefrom the adaptive filter 520. A skilled artisan will, however,appreciate that the adaptation step size adaptor 540 can be integratedwith the adaptive filter 520.

The embodiment described in connection with FIG. 5 can be combined withone or more of the embodiments described above in connection with FIGS.3, 4A, and 413, which can further speed up the convergence of theadaptive filter 520. For example, the embodiment of FIG. 5 can becombined with the model reduction technique of FIG. 3. The embodiment ofFIG. 5 can be combined with different adaptation step sizes fordifferent taps and/or adaptation step size varying over time describedabove in connection with FIGS. 4A and 4B. The embodiment of FIG. 5 canbe combined with both (1) the model reduction technique of FIGS. 3, and(2) different adaptation step sizes for different taps and/or adaptationstep size varying over time described above in connection with FIGS. 4Aand 4B.

EXAMPLES

In Example 1, a center frequency (a measure of a central frequencybetween the upper and lower cutoff frequencies) f_(c) of 875 MHz, a 100MHz ADC, and a 7th-order Butterworth low pass filter were used for an RFreceiver with no compensation. The measured results from actual hardwaremeasurement are shown in FIG. 6, which shows a frequency response forone particular silicon sample of the receiver design, and the imagerejection ratios for different sample silicon chips with the saidreceiver design.

In Example 2, a center frequency f_(c) of 875 MHz, a 100 MHz ADC, and a7^(th)-order Butterworth low pass filter were used with a combination ofthe embodiments of FIGS. 3-5. In Example 2, an adaptive filter by modelreduction was provided with normalized variable adaptation step sizesper tap and over time. The result is shown in FIG. 7 in solid lines,which shows image rejection ratios 710 and frequency responses 720. TheExample 2 shows greater image rejection ratios (at least 45 dB) over awider frequency band than those of Anttila et al. Further, the Example 2shows convergence time of about 100 msec.

Further, the adaptive filter of the Example 2 exhibited that theconvergence time was reduced from 2-3 seconds (Anttila et al.) to about100 msec. Further, the complexity of the filter was reduced byapproximately ½ since only w(0) is a complex number.

Alternative Embodiments

Referring to FIG. 8, an I/Q imbalance compensation module according toanother embodiment will be described below. The illustrated I/Qimbalance compensation module 800 includes a first node 801, a secondnode 802, a first complex conjugation block 810, a second complexconjugation block 815, an adaptive filter 820, a delay element 825, afilter adaptation block 827, an adder 830, and an adaptation step sizeadaptor 840. FIG. 8 shows only one example of alternative configurationsthat are mathematically equivalent to the I/Q imbalance compensationmodules of FIGS. 3, 4A and 5. A skilled artisan will appreciate thatthere are many other alternative configurations mathematicallyequivalent to the I/Q imbalance compensation modules of FIGS. 3, 4A and5.

A complex digital signal x[n] is provided to the first node 801 from theI and Q paths of a receiver, such as the I and Q paths of FIG. 1. Thedigital signal x[n] is provided to the adder 830 and the adaptive filter820. The adaptive filter 820 receives a feedback signal generated froman output signal y[n] through the delay element 825, the filteradaptation block 827, the adaptation step size adaptor 840, and thesecond complex conjugation block 815 to update values of filtercoefficients w[n].

The adaptive filter 820 can perform a convolution operation on thecomplex digital signal x[n] and the filter coefficients w[n] to generatean intermediate signal. The intermediate signal from the adaptive filter820 is provided to the first complex conjugation block 810. A complexconjugate of the intermediate signal is generated by the first complexconjugation block 810, and is provided to the adder 830 to reduce orcancel I/Q imbalance in the complex digital signal x[n]. The illustratedI/Q imbalance compensation module 800 can be mathematically equivalentto one of the I/Q imbalance compensation modules 300, 400, 500 of FIG.3, 4A, or 5.

In the illustrated embodiment, (1) the model reduction described inconnection with FIG. 3 and/or (2) one or more of the variable adaptationstep size schemes described in connection with 4A-5 can be used foreffective I/Q imbalance compensation. In an embodiment in which only themodel reduction is used, the adaptation step size adaptor is omitted.

Referring to FIG. 9, an I/Q imbalance compensation module according toyet another embodiment will be described below. The illustrated I/Qimbalance compensation module 900 includes a first node 901, a secondnode 902, a first complex conjugation block 910, a second complexconjugation block 915, an adaptive filter 920, a delay element 925, afilter adaptation block 927, an adder 930, and an adaptation step sizeadaptor 940.

A complex digital signal x[n] is provided to the first node 901 from theI and Q paths of a receiver, such as the I and Q paths of FIG. 1. Thedigital signal x[n] is provided to the first complex conjugation block910, which generates a complex conjugate of the digital signal x[n]. Thecomplex conjugate of the digital signal x[n] is provided to the adder930.

The complex digital signal x[n] is also provided to the adaptive filter920. The adaptive filter 920 receives a feedback signal generated froman intermediate signal u[n] outputted from the adder 930 through thedelay element 925, the filter adaptation block 927, and the adaptationstep size adaptor 940 to update values of filter coefficients w[n].

The adaptive filter 920 can perform a convolution operation on thecomplex digital signal x[n] and the filter coefficients w[n] to generatea filter output signal. The filter output signal from the adaptivefilter 920 is provided to the adder 930 to reduce or cancel I/Qimbalance in the complex conjugate of the complex digital signal x[n].The intermediate signal u[n] outputted from the adder 930 is provided tothe second complex conjugation block 915 to generate an output signaly[n]. The illustrated I/Q imbalance compensation module 900 can bemathematically equivalent to one of the I/Q imbalance compensationmodules 300, 400, 500, 900 of FIG. 3, 4A, 5, or 9.

In the illustrated embodiment, (1) the model reduction described inconnection with FIG. 3 and/or (2) one or more of the variable adaptationstep size schemes described in connection with 4A-5 can be used foreffective PQ imbalance compensation. In an embodiment in which only themodel reduction is used, the adaptation step size adaptor is omitted.

Referring to FIG. 10, an I/Q imbalance compensation module according toyet another embodiment will be described below. The illustrated I/Qimbalance compensation module 1000 includes a first node 1001, a complexconjugation block 1010, an adaptive filter 1020, an adder 1030, and afeed forward block 1060.

A complex digital signal x[n] is provided to the first node 1001 fromthe I and Q paths of a receiver, such as the I and Q paths of FIG. 1.The digital signal x[n] is provided to the first complex conjugationblock 1010, which generates a complex conjugate of the digital signalx[n], which is then provided to the adaptive filter 1020. The digitalsignal x[n] is also provided to the adder 1030.

The adaptive filter 1020 receives a feed forward signal generated fromthe feed forward block 1060 to update values of filter coefficientsw[n]. The feed forward block 1060 can generate the feed forward signal,using only the second-order statistics of the digital signal x[n].Details of using only the second-order statistics of the digital signalx[n] are described at pages 2105 and 2106 of Anttila et al.,“Circularity-Based I/Q Imbalance Compensation in WidebandDirect-Conversion Receivers,” IEEE Transactions on Vehicular Technology,Vol. 57, No. 4, pp. 2099-2113 (July 2008).

The feed forward block 1060 serves to null complementary autocorrelationof an output signal for the span of the compensation filter (N samples),E[y(n)y(n)]=0, which is equivalent to Equation 12.

c ₁₀₂+Γ_(χ) w+ Γ _(χ) w+WC* _(χ) w=0  Equation 12

In Equation 12, c_(x) ΔE[x(n)x(n)]=[c_(x)(0), c_(x)(1), . . .c_(x)(N−1)]^(T) with x(t) Δ [x(n) x(n−1), . . . , x(n−N+1)]^(T). Γ_(x),Γ _(x), C_(x), and W are defined below in Equation 13-a to 13-d.

$\begin{matrix}{\mspace{79mu} {\Gamma_{x}\overset{\Delta}{=}\begin{bmatrix}{\gamma_{x}(0)} & {\gamma_{x}(1)} & \ldots & {\gamma_{x}( {N - 1} )} \\{\gamma_{x}^{*}(1)} & {\gamma_{x}(0)} & \ldots & {\gamma_{x}( {N - 2} )} \\\vdots & \vdots & \ddots & \vdots \\{\gamma_{x}^{*}( {N - 1} )} & {\gamma_{x}^{*}( {N - 2} )} & \ldots & {\gamma_{x}(0)}\end{bmatrix}}} & {{Equation}\mspace{14mu} 13\text{-}a} \\{\mspace{79mu} {{\overset{\_}{\Gamma}}_{x}\overset{\Delta}{=}\begin{bmatrix}{\gamma_{x}(0)} & {\gamma_{x}(1)} & \ldots & {\gamma_{x}( {N - 1} )} \\{\gamma_{x}(1)} & {\gamma_{x}(2)} & \ldots & {\gamma_{x}(N)} \\\vdots & \vdots & \ddots & \vdots \\{\gamma_{x}( {N - 1} )} & {\gamma_{x}(N)} & \ldots & {\gamma_{x}( {{2N} - 2} )}\end{bmatrix}}} & {{Equation}\mspace{14mu} 13\text{-}b} \\{C_{x}\overset{\Delta}{=}{\quad\begin{bmatrix}{c_{x}(0)} & {c_{x}(1)} & {c_{x}(2)} & \ldots & {c_{x}( {N - 1} )} \\{c_{x}(1)} & {c_{x}(0)} & {c_{x}(1)} & \ldots & {c_{x}( {N - 2} )} \\{c_{x}(2)} & {c_{x}(1)} & {c_{x}(0)} & \ldots & {c_{x}( {N - 3} )} \\\vdots & \vdots & \vdots & \; & \vdots \\{c_{x}( {{2N} - 2} )} & {c_{x}( {{2N} - 3} )} & {c_{x}( {{2N} - 4} )} & \ldots & {c_{x}( {N - 1} )}\end{bmatrix}}} & {{Equation}\mspace{14mu} 13\text{-}c} \\{\mspace{79mu} {W\overset{\Delta}{=}\begin{bmatrix}w^{T} & 0 & \ldots & 0 \\0 & w^{T} & \ldots & 0 \\\vdots & \; & \ddots & \vdots \\0 & 0 & \ldots & w^{T}\end{bmatrix}}} & {{Equation}\mspace{14mu} 13\text{-}d}\end{matrix}$

N represents the number of taps or filter coefficients of the adaptivefilter 1020 (vector w). The matrix C_(x) has dimensions (2N−1)×N. MatrixW, which is constructed from the adaptive filter coefficients, has asize N×(2N−1). A solution to Equation 12 can be computed iteratively. Inone embodiment, the last term WC_(x)*w on the left-hand side of Equation12 can be ignored, and the filter coefficients w of the adaptive filter1020 can be obtained from Equation 14 below.

w=−(Γ_(χ)+ Γ _(χ))⁻¹ c _(χ)  Equation 14

The adaptive filter 1020 can perform a convolution operation on thecomplex conjugate x*[n] of the digital signal x[n] and the filtercoefficients w[n] to generate a filter output signal. The filter outputsignal from the adaptive filter 1020 is provided to the adder 1030 toreduce or cancel I/Q imbalance in the complex digital signal x[n],thereby generating an output signal y[n]. In the illustrated embodiment,the model reduction technique described in connection with FIG. 3 can beused for effective I/Q imbalance compensation. A skilled artisan willappreciate that there are other ways of solving, either exactly orapproximately, Equation (12), and that the model reduction techniquedescribed above can also apply to the other ways.

Applications

The embodiments described above can be effectively used for wide-band RFreceivers covering from DC to about −3 dB corners, operating at afrequency of, for example, about 50 MHz to about 100 MHz. Theconfigurations and principles of the embodiments can also be adapted forany other electronic devices, such as transceivers or receivers (forexample, direct conversion receivers, super-heterodyne receivers, andlow intermediate frequency receivers), that can use I/Q imbalancecompensation for a quadrature path.

The circuits employing the above described configurations can beimplemented into various electronic devices or integrated circuits.Examples of the electronic devices can include, but are not limited to,consumer electronic products, parts of the consumer electronic products,electronic test equipments, etc. Examples of the electronic devices canalso include cable modems, wireless devices, and networking equipment.The consumer electronic products can include, but are not limited to, amobile phone, cellular base stations, a telephone, a television, acomputer monitor, a computer, a hand-held computer, a netbook, a tabletcomputer, a digital book, a personal digital assistant (PDA), a stereosystem, a cassette recorder or player, a DVD player, a CD player, a VCR,a DVR, an MP3 player, a radio, a camcorder, a camera, a digital camera,a portable memory chip, a copier, a facsimile machine, a scanner, amulti functional peripheral device, a wrist watch, a clock, etc.Further, the electronic device can include unfinished products.

The foregoing description and claims may refer to elements or featuresas being “connected” or “coupled” together. As used herein, unlessexpressly stated otherwise, “connected” means that one element/featureis directly or indirectly connected to another element/feature, and notnecessarily mechanically. Likewise, unless expressly stated otherwise,“coupled” means that one element/feature is directly or indirectlycoupled to another element/feature, and not necessarily mechanically.Thus, although the various schematics shown in the figures depictexample arrangements of elements and components, additional interveningelements, devices, features, or components may be present in an actualembodiment (assuming that the functionality of the depicted circuits isnot adversely affected).

Although this invention has been described in terms of certainembodiments, other embodiments that are apparent to those of ordinaryskill in the art, including embodiments that do not provide all of thefeatures and advantages set forth herein, are also within the scope ofthis invention. Moreover, the various embodiments described above can becombined to provide further embodiments. In addition, certain featuresshown in the context of one embodiment can be incorporated into otherembodiments as well. Accordingly, the scope of the present invention isdefined only by reference to the appended claims.

1. An apparatus comprising: a finite impulse response (FIR) filterconfigured to filter a version of a digital signal to generate acompensation signal, wherein the FIR filter has X real number filtercoefficients and Y imaginary number coefficients, wherein Y is less thanX, wherein the digital signal comprises a digital representation of ademodulated in-phase and quadrature phase component of a radio frequency(RF) signal; and an adder configured to sum another version of thedigital signal and a version of the compensation signal to generate abalanced digital signal that has an improved image rejection ratioversus the digital signal; wherein one of the versions of the digitalsignal or the version of the compensation signal is a complex conjugateof the digital signal or a complex conjugate of the compensation signal,respectively, and the others are not the complex conjugates, wherein theFIR filter and the adder comprise electronic hardware.
 2. The apparatusof claim 1, wherein the FIR filter has only 1 imaginary numbercoefficient and the 1 imaginary number coefficient is present only forthe first tap of the FIR filter.
 3. The apparatus of claim 1, furthercomprising analog low-pass filters for anti-aliasing ofanalog-to-digital converters that generate components of the digitalsignal, wherein the analog low-pass filters have all-poleconfigurations.
 4. The apparatus of claim 1, further comprising acomplex conjugation circuit configured to perform a complex conjugationoperation on the digital signal or the compensation signal to generateone of the versions of the digital signal or the version of thecompensation signal, respectively.
 5. The apparatus of claim 4, whereinthe complex conjugation circuit generates a complex conjugate of thedigital signal, and provides the complex conjugate of the digital signalto the FIR filter.
 6. The apparatus of claim 5, further comprising: adelay element configured to delay the balanced digital signal; and afilter adaptation block configured to generate a feedback signal fromthe delayed balanced digital signal, and to provide the feedback signalto the FIR filter for updating the real and imaginary number filtercoefficients.
 7. The apparatus of claim 5, further comprising a feedforward block configured to generate a feed forward signal from thedigital signal, and to provide the feed forward signal to the FIR filterfor updating the real and imaginary number filter coefficients.
 8. Theapparatus of claim 4, wherein the FIR filter is configured to providethe complex conjugation circuit with the compensation signal byfiltering the digital signal, and wherein the complex conjugationcircuit is configured to provide the adder with a complex conjugate ofthe compensation signal.
 9. The apparatus of claim 8, furthercomprising: a delay element configured to delay the balanced digitalsignal; a filter adaptation block configured to generate a feedbacksignal using the delayed balanced digital signal; and a second complexconjugation circuit to provide a complex conjugate of the feedbacksignal to the FIR filter for updating the real and imaginary numberfilter coefficients.
 10. The apparatus of claim 4, wherein the FIRfilter is configured to provide the adder with the compensation signalby filtering the digital signal, and wherein the complex conjugationcircuit provides the adder with a complex conjugate of the digitalsignal.
 11. The apparatus of claim 10, further comprising: a delayelement configured to delay the balanced digital signal; a filteradaptation block configured to generate a feedback signal using thedelayed balanced digital signal, and to provide the feedback signal tothe FIR filter for updating the real and imaginary number filtercoefficients.
 12. The apparatus of claim 1, further comprising anadaptation step size adaptor for providing two or more differentadaptation step sizes for updating the filter coefficients.
 13. Theapparatus of claim 1, further comprising an adaptation step size adaptorfor varying adaptation step sizes for one or more of the filtercoefficients over time in updating the filter coefficients.
 14. Theapparatus of claim 1, further comprising an adaptation step size adaptorfor dividing adaptation step sizes for one or more of the filtercoefficients by the square norm of the balanced digital signal inupdating the filter coefficients.
 15. A method of improving an imagerejection ratio of a digital signal having demodulated in-phase andquadrature-phase components of a radio frequency signal, the methodcomprising: filtering a version of the digital signal with a finiteimpulse response (FIR) filter to generate a compensation signal, whereinthe FIR filter has X real number filter coefficients and Y imaginarynumber coefficients, wherein Y is less than X, wherein filtering isimplemented by hardware or by instructions implemented by a processor;generating a complex conjugate of the digital signal or the compensationsignal; and summing another version of the digital signal and a versionof the compensation signal to generate a balanced digital signal thathas an improved image rejection ratio versus the digital signal, whereinone of the versions of the digital signal and the version of thecompensation signal corresponds to a complex conjugate of the digitalsignal or the compensation signal, respectively, and the others are notthe complex conjugates.
 16. The method of claim 15, wherein the FIRfilter has only 1 imaginary number coefficient, wherein the imaginarynumber coefficient is present only for the first tap of the FIR filter.17. The method of claim 15, further comprising performing anti-aliasingfiltering of the demodulated in-phase component and the demodulatedquadrature-phase component by filtering with analog low-pass filtersthat have all-pole configurations prior to analog-to-digital conversionsused to generate the digital signal.
 18. The method of claim 15, furthercomprising generating one of the versions of the digital signal byperforming a complex conjugation of the digital signal.
 19. The methodof claim 15, further comprising: delaying the balanced digital signal;generating a feedback signal by multiplying the delayed balanced digitalsignal with an adaptation step size; and determining the X real numbercoefficients and Y or fewer imaginary number coefficients, using thefeedback signal.
 20. An apparatus comprising: an (N+1)-th order finiteimpulse response (FIR) filter configured to filter a version of adigital signal to generate a compensation signal, wherein the FIR filterhas N taps, N real number filter coefficients, and N−1 or fewerimaginary number coefficients, wherein the digital signal comprises adigital representation of a demodulated in-phase and quadrature phasecomponent of a radio frequency (RF) signal; means for generating acomplex conjugate of the digital signal or the compensation signal; andmeans for summing another version of the digital signal and a version ofthe compensation signal to generate a balanced digital signal that hasan improved image rejection ratio versus the digital signal, wherein oneof the versions of the digital signal and the version of thecompensation signal corresponds to a complex conjugate of the digitalsignal or the compensation signal, respectively, and the others are notthe complex conjugates.
 21. The apparatus of claim 20, wherein the FIRfilter has only 1 imaginary number coefficient, wherein the imaginarynumber coefficient is present only for the first tap of the FIR filter.22. The apparatus of claim 20, further comprising means for generatingone of the versions of the digital signal by performing a complexconjugation of the digital signal.
 23. The apparatus of claim 20,further comprising: means for delaying the balanced digital signal; andmeans for generating a feedback signal by multiplying the delayedbalanced digital signal with an adaptation step size; and wherein theFIR filter is configured to determine the filter coefficients, using thefeedback signal.
 24. An apparatus comprising: a finite impulse response(FIR) filter configured to filter a version of a digital signal togenerate a compensation signal, wherein the FIR filter has X real numberfilter coefficients and X imaginary number coefficients, wherein atleast one, but not all, of the imaginary number coefficients is 0,wherein the digital signal comprises a digital representation of ademodulated in-phase and quadrature phase component of a radio frequency(RF) signal; and an adder configured to sum another version of thedigital signal and a version of the compensation signal to generate abalanced digital signal that has an improved image rejection ratioversus the digital signal; wherein one of the versions of the digitalsignal or the version of the compensation signal is a complex conjugateof the digital signal or a complex conjugate of the compensation signal,respectively, and the others are not the complex conjugates, wherein theFIR filter and the adder comprise electronic hardware.